Math 3GR3 - Abstract Algebra
(Fall 2026)

This course is an introduction to groups and rings with an emphasis on examples.

News/Schedule Homework SAGE Quizzes Handouts Grading Scheme Dates Policies

Course Information

Instructor: Adam Van Tuyl

Office: Hamilton Hall 419
Office Hours: TBD
Email: vantuyl@math.mcmaster.ca

Place and Time:

Class: Monday, Wednesday 8:30-9:20 and Friday 10:30-11:20. See MOSAIC for location
Tutorial: Tuesday 12:30-1:20 See MOSAIC for location

Textbook:

• Abstract Algebra: Theory and Applications (2023 Edition)
  by Tom Judson. This is a FREE online textbook. Hard copies can also be found in the bookstore or at online retailers like Amazon. Here is an online version. Note that we will be using the 2023 edition but older editions can be used.

Optional Textbooks:

The following books may be helpful.

• Mathematical Writing
  by Franco Vivaldi. This book will help you write proofs. An electronic copy is FREE through the McMaster library.
• How to Think about Abstract Algebra
  by Lara Alcock. This book has many useful examples and discusses ``how'' to prove results in abstract algebra.

News/Schedule (Last Updated: July 22, 2026)

Below is a summary of what we did in class, plus any relevant news and/or information.

• July 13, 2026 I started to set up the website for Fall 2026. Please check back for more details!

Here is a proprosed schedule (I will update as the semester goes along):

Math 3GR3 Schedule
Week 1 (Sept 7-11)
Homework: * Read 1.1 and 1.2 * Start Assignment 1 (due: Sept 25)
Lecture	Topic	Practice Problems
Lecture 1	Introduction to Abstract Algebra 1.1 Set Theory Review	Sec. 1.4 -- 1, 6, 12, 17, 18
Lecture 2	1.2 Equivalence Relations	Sec. 1.4 -- 18, 22bc, 24b, 25, 28
Week 2 (Sept 14-18)
Homework: * Read 2.1 and 2.2 * Quiz 1 on Sept 15 in Tutorial on Chapter 1 and Mathematical Writing * Submit Assignment 0 (Due Sept 18) [Optional] * Work on Assignment 1 (Due Sept 25)
Lecture 3	2.2 Division Algorithm Proof writing Review	Sec. 2.4 -- 22
Lecture 4	2.1 Review of Induction 2.2 Euclidean Algorithm	Sec. 2.4 -- 1, 3, 5, 9, 15ab, 23
Lecture 5	2.2 Prime Numbers	Sec. 2.4 -- 18, 19, 26, 28
Week 3 (Sept 21-25)
Homework: * Read 3.1, 3.2, and 3.3 * Submit Assignment 1 (Due Sept 25) via Crowdmark
Lecture 6	3.1 Examples of Groups	Sec. 3.5 -- 1a 3b, 3, 6
Lecture 7	3.2 Definition of Groups	Sec. 3.5 -- 10, 11, 12, 13
Lecture 8	3.2 Basic Properties of Groups 3.3 Subgroups	Sec. 3.5 -- 25, 26, 27, 32, 33
Week 4 (Sept 28-Oct 2)
Homework: * Read 3.3, 4.1 * Quiz 2 on Sept 28 in Tutorial * Work on Assignment 2 (Due Oct 9)
Lecture 9	3.3 Subgroups 4.1 Cyclic Subgroups	Sec 3.5 -- 42, 45, 46, 47, 54
	No class Sept 30
Lecture 10	4.1 Cyclic Subgroups	Sec. 4.5 -- 1, 2def, 3bij, 5, 11
Week 5 (Oct 5-9)
Homework: * Read 4.2, 5.1 * Submit Assignment 2 (Due Oct. 9) via Crowdmark * Start studying for Midterm 1 (Oct. 23) -- here is a Review Sheet
Lecture 11	4.2 Multiplicative Groups and Complex Numbers	Sec. 4.5 -- 20, 23, 30, 39
Lecture 12	5.1 Permutation Groups	Sec. 5.4 - 1, 2abc, 4, 12, 13, 17
Lecture 13	5.1 Alternating Groups
Week 6 (Oct 12-16)
Reading Week (No Classes)
Week 7 (Oct 19-23)
Homework: * Read 5.2, 6.1 * Study for Midterm 1 (Oct. 23) -- here is a Review Sheet
Lecture 14	5.2 Dihedral Groups
Lecture 15	6.1 Cosets and Lagrange's Theorem
Lecture 16	Midterm I

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Homework

There will be five homework assignments. Assignments must conform to the guidelines in the course outline. Your homework will be graded as follows:

1. For every assignment, 3 or 4 questions will graded in detail (e.g., you are required to write complete mathematical proofs). These questions will be graded out of 5 pts using the rubric described in the course handout.
2. The remaining questions will be graded for completion (1pt each)

Assignments are posted below. Assignments will be submitted via Crowdmark. You will receive an email to your McMaster account that you will use to upload your assignment. All assignments due by 11:59PM on the due date.

• Assignment 0 (Due: Sept. 18) [Optional]
• Assignment 1 (Due: Sept. 25)
• Assignment 2 (Due: Oct. 9)

For more information on writing proofs, the following notes may help:

• Guide to writing proofs
  A handout on writing proofs I wrote for algebra in 2010.
• Some remarks on writing mathematical proofs
  A nice short guide to writing mathematics by John M. Lee.

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SAGE

As part of this course, the assignments may make use of SAGE, an open-source mathematics program. For the assignments, I may ask you to work through the relevant SAGE tutorials found the book's webpage. You can download your own version of SAGE, or you can try to use CoCalc. Alternatively, you can use the following shell to test your code. This shell allows you to do small calculations.

The following links may help:

• For tutorials, more information on SAGE, and even a free book on SAGE and mathematics, see George Bard's SAGE website
• SAGE's documentation for group theory

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Quizzes

There will be five quizzes. Each quiz will be about 20 minutes in length, and will be held during tutorial. The provisional dates of the quizzes are

• Quiz 1 - September 15
• Quiz 2 - September 29
• Quiz 3 - October 27
• Quiz 4 - November 10
• Quiz 5 - December 1

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Handouts

All class handouts are available as PDF files.

Course Information
Course handout from first day of class [Link to SimpleSyllabus]

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Grading Scheme

I will calculate your mark using two different weightings. Your final mark will be the higher of the two weights.

Weighting 1
10% = Assignments (4 x 2.5%) [Best 4 of 5]
10% = Quizzes (4 x 2.5%) [Best 4 of 5]
35% = Midterms (2 x 17.5%)
45% = Final Exam

Weighting 2
10% = Assignments (4 x 2.5%) [Best 4 of 5]
10% = Quizzes (4 x 2.5%) [Best 4 of 5]
17.5% = Midterm [Best 1 of 2]
62.5% = Final Exam

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Important Dates

Sept. 8, 2026
First semester classes begin

Oct. 12-16, 2026
Fall break (no classes)

Oct. 23, 2026
Midterm 1

Nov. 20, 2026
Midterm 2

Dec. 9, 2026
First semester classes end

Dec. 11-23, 2026
Final Exams

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Class Polices

For all official policies, including information about MSAF, please consult the Official Math 3GR3 Course Outline